Reflecting image-dependent SDEs in Wasserstein space and large deviation principle

In this article, we study a class of reflecting stochastic differential equations whose coefficients depend on image measures of solutions under a given initial measure in Wasserstein space . By the penalization method, the image process, which is a diffusion process in , is constrained in a priori given domain . The large deviation principle for this reflecting image process is also established by weak convergence method.